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Bayesian View Of Solar Neutrino Oscillations

We present the results of a Bayesian analysis of solar neutrino data in terms of nu_e->nu_{mu,tau} and nu_e->nu_s oscillations, where nu_s is a sterile neutrino. We perform a Rates Analysis of the rates of solar neutrino experiments, including the first SNO CC result, and spectral data of the CHOOZ experiment, and a Global Analysis that takes into account also the Super-Kamiokande day and night electron energy spectra. We show that the Bayesian analysis does not suffer any problem from the inclusion of the numerous bins of the CHOOZ and Super-Kamiokande energy spectra and allows to reach the same conclusions on the favored type of neutrino transitions and on the determination of the most favored values of the oscillation parameters in both the Rates and Global Analysis. Our Bayesian analysis shows that nu_e->nu_s transitions are strongly disfavored with respect to nu_e->nu_{mu,tau} transitions. In the case of nu_e->nu_{mu,tau} oscillations, the LMA region is favored by the data (86% probability), the LOW region has some small chance (13% probability), the VO region is almost excluded (1% probability) and the SMA region is practically excluded (0.01% probability). We calculate also the marginal posterior probability distributions for tan^2 theta and Delta m^2 and we show that the data imply large mixing almost with certainty and large values of Delta m^2 are favored. We present also the results of a standard least-squares analysis and we show that the standard goodness of fit test is not able to rejects pure nu_e->nu_s transitions. The likelihood ratio test allows to reject pure nu_e->nu_s transitions in favor of nu_e->nu_{mu,tau} transitions only in the Global Analysis.